The Computational Universe

In the 1940s, computer pioneer Konrad Zuse began to speculate that
the universe might be nothing but a giant computer continually
executing formal rules to compute its own evolution. He published
the first paper on this radical idea in 1967, and since then it has
provoked an ever-increasing response from popular culture (the film
The Matrix, for example, owes a great deal to Zuse's
theories) and hard science alike.

Given this backdrop, Seth Lloyd appears to be exaggerating when he
claims in his informative and entertaining new book that he
"advocates a new paradigm" by postulating the universe to
be a machine that processes information. However, in the book, which
is titled Programming the Universe, Lloyd does somewhat
distinguish himself from his predecessors by focusing on the weird
world of quantum computation. He lucidly explains what quantum
computation is all about, how the process of quantum entanglement
seems to involve an instantaneous exchange of information between
locations that can be light-years apart, and why this phenomenon
unfortunately cannot be exploited to transmit information faster
than light. He also describes how quantum computers would be able to
solve certain problems much faster than their traditional counterparts.

The book's central conceit is that the universe can be viewed as a
giant quantum computer made up of connected quantum gates that flip
quantum bits and thereby propagate information and uncertainty in an
"infectious" way. Lloyd uses results by Hans Joachim
Bremermann, Norman Margolus and Lev Levitin to calculate the
processing power of the "ultimate laptop" (one with 1
kilogram of mass and 1 liter of volume): a maximum of
1051 operations per second on 1032 bits. A
good fan would be needed, though: The massively parallel laptop
would be roughly 100 times hotter than the center of the Sun. Lloyd
also calculates that the visible universe has so far computed about
10122 operations on 1092 bits. Doesn't sound
like a lot, does it?

Like most quantum physicists, Lloyd believes that there is a source
of true randomness, which manifests itself whenever we measure a
quantum bit. He does not explicitly mention, however, that this
belief has never been experimentally proved. Neither Heisenberg's
uncertainty principle nor Bell's inequality (which rests on the very
assumption of randomness) excludes the possibility that the universe
(including all observers inhabiting it) is in principle computable
by a deterministic computer, as first suggested by Zuse.

In fact, Lloyd's belief in true randomness also seems inconsistent
with his invocation of Ockham's razor, which favors simple
explanations of the universe's history over complex ones. According
to both standard and algorithmic information theory, true randomness
actually corresponds to maximal information, complexity and
description length—the opposite of simplicity.

As long as the (currently somewhat unfashionable) hypothesis of
determinism remains unfalsified, many scientists will be
dissatisfied by an explanation of our universe's history that
requires an enormous amount of information to describe all the
random events that have taken place, in addition to the known,
compactly describable physical laws. Physicists should keep
searching for simple, deterministic, pseudorandom computational
rules explaining any type of hitherto-unexplained apparent
randomness. Einstein, whose belief that "God does not play
dice" has not yet been proved wrong, would probably agree.

The book is least convincing when it comes to the topics of
complexity, entropy and algorithmic information. Lloyd compares
random events at the quantum level to monkeys typing a random
program on the universal computer; this is linked to Ray
Solomonoff's basic concept of algorithmic probability
theory—namely, that short random programs are more likely than
long ones. However, the point of Solomonoff's approach is that some
programs can remain short by ceasing to read new input bits. This
essential feature seems absent from Lloyd's setup, which demands the
permanent creation of new bits corresponding to never-ending
programs, thus making each "program" extremely unlikely.

Of all the various complexity measures, Lloyd explicitly favors
those that combine the difficulty of doing something with the
difficulty of describing it. The obvious choice here would be Leonid
A. Levin's Kt-complexity (and its probabilistic derivative, the
Speed Prior), which trades off space and computation time in a way
that is theoretically optimal in a certain sense. Lloyd, however,
does not even mention it. Instead he focuses on measures based on
Charles H. Bennett's logical depth, and something called
"effective complexity," which reflects a preliminary
attempt of physicist Murray Gell-Mann and Lloyd himself to hide the
complexity of truly random bits. Generally speaking, the connections
between Lloyd's model of quantum processing and algorithmic
information theory seem vague.

Some of Lloyd's statements reflect a certain naiveté about
some topics in computer science. For example, he writes that
"According to the Church-Turing hypothesis, every possible
mathematical structure is represented in some component of the
superposition" of all possible computations, despite the fact
that much of mathematics deals with incomputable objects. Other
incorrect statements include this one: "In fact, every
universal computer can be shown not only to simulate every other
universal computer, but to do so efficiently."

Lloyd's historical notes on computation and bits refer to Charles
Babbage's analytic engine and John Napier's logarithmic bones but
fail to mention Gottfried Wilhelm Leibniz, the inventor of the bit
(1700), and Wilhelm Schickard, constructor of the very first
(non-program-controlled) computer, in 1623. For some reason Lloyd
also seems to give equal credit to Zuse and Ed Fredkin as creators
of the "universe as a computer" idea, although Fredkin got
into this business long after Zuse. On the other hand, Lloyd did
enrich my understanding by pointing out that the "many
worlds" theory (usually attributed to the physicist Hugh
Everett) can be traced back to poet and novelist Jorge Luis Borges.

Lloyd spices his story with interesting and sometimes touching
personal tales of his career at the border between computer science
and physics. Despite my few quibbles, I recommend this well-written
book without hesitation to anybody interested in an overview of
basic ideas in the field. I intend to buy a few copies as presents
for my friends.